1.1 Variables in Algebra : 1.1 Variables in Algebra Mr. Cashill
Verona High School
Definitions : Definitions Variable--A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number.
Variable expression (A.K.A. - Algebraic Expression)--An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign)
Evaluate a Variable Expression--Write the expression, substitute a number for each variable, and simplify the result.
How Do You Describe a Variable Expression? : How Do You Describe a Variable Expression?
State the meaning of the variable expression and name the operation : State the meaning of the variable expression and name the operation A A A A Please click to bypass answer slide
Answer:State the meaning of the variable expression and name the operation : Answer:State the meaning of the variable expression and name the operation 8 minus x; Subtraction
2 times w; Multiplication
7 divided by n; Division
6 plus p; Addition You must click on the answer to return to the previous slide Click in the middle of the window to view each answer
Slide 6: More Variable Expressions or Algebraic Expressions An algebraic expression can
consist of one or more numbers
and variables along with one or
more arithmetic operations.
Slide 7: More Variable Expressions or Algebraic Expressions Examples: Algebraic Expressions **Verbal Expression a divided by b; minus 7
(note: fractions are division problems) r times the product of 4 and k
(note: multiplication is implied when two or more
letters xy or numbers 4k are together and there
is no operation symbol). The product of 5xy divided by 3z The sum of 4 and n; divided by m **Verbal expressions are usually more detailed than stating the meaning. Verbal expressions are used to translate words or language into variable or algebraic equations. They consist of key words that help identify the type of equation that will need to be simplified. These key words are usually introduced when writing variable expressions and writing equations for problem solving.
Slide 8: Evaluate a Variable Expression Evaluate a Variable Expression: Write the expression, substitute a number for each variable and simplify the result.
Value of a Variable:
A number that may be substituted or assigned to a particular variable such as n = 3 or x = 5.
Slide 9: Evaluate a Variable Expression Example 1: Evaluate each expression when n = 4 Substitute 4 for n. Simplify Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Substitute 4 for n. Simplify Solution:
Slide 10: Evaluate a Variable Expression Example 2: Evaluate each expression when x = 8 Substitute 8 for x. Simplify Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Solution: Note: No operation sign between a variable and number indicates a multiplication problem. Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are: Substitute 8 for x. Simplify Recall that division problems are also fractions – this problem could be written as:
Slide 11: Evaluate a Variable Expression Example 3: Evaluate each expression given x = 4, y = 6, z = 24. Substitute 4 for x; 6 for y. simplify Solution: Recall: No operation sign between variable(s) and a number indicates multiplication problem.
xy means 4(6);
5xy means 5(4)(6) Solution: Recall:
Slide 12: Evaluate a Variable Expression You Try IT: Evaluate each expression when a = 6, b = 12, and c = 3 A A A A A A
Slide 13: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Notice that all the numbers and letters are together and that there are no operation symbols which indicates that this is a multiplication problem. Substitute the value for a = 6 and c = 3 into the problem and multiply Multiply Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer
Slide 14: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Division Problem Substitute the value for a = 6 and c = 3 into the problem and divide Simplified Click to return to “You try it” slide Another way to solve division problems is to write them as fractions and simplify. Click in the middle of the window to view each answer
Slide 15: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Addition Problem Substitute the value for a = 6, b=12, and c = 3 into the problem, then add Simplified Add Click to return to “You try it” slide Click in the middle of the window to view each answer
Slide 16: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Multiplication Problem Substitute the value for b=12 and a = 6 into the problem, then multiply Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer
Slide 17: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Subtraction Problem Substitute the value for b=12 and a = 3 into the problem, then Subtract Simplified Click to return to “You try it” slide Click in the middle of the window to view each answer
Slide 18: Evaluate each expression when a = 6, b = 12, and c = 3 Evaluate a Variable Expression You Try IT: Answers Division Problem Substitute the value for c=3 and b = 12 into the problem, then Divide
Note: It is better to rewrite this division problem as a fraction.
This fraction can now be reduced to its simplest form. Simplified Divide both numerator and denominator by the GCF = (3) to reduce this fraction. It is OK to have a fraction as an answer. Click in the middle of the window to view each answer Click to return to “You try it” slide
Slide 19: x + 17 = 25 8 x = 8 x – 3 = 4 Variables: Summary and Review 1 Substitute the numerical value of a variable into an algebraic expression 2 “Solve the equation for x.” x = 4 1